TSTP Solution File: REL050+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL050+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:54:33 EDT 2022
% Result : Theorem 2.22s 2.49s
% Output : Refutation 2.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : REL050+2 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jul 8 08:29:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.47/1.04 ============================== Prover9 ===============================
% 0.47/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.47/1.04 Process 7106 was started by sandbox on n015.cluster.edu,
% 0.47/1.04 Fri Jul 8 08:29:21 2022
% 0.47/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_6952_n015.cluster.edu".
% 0.47/1.04 ============================== end of head ===========================
% 0.47/1.04
% 0.47/1.04 ============================== INPUT =================================
% 0.47/1.04
% 0.47/1.04 % Reading from file /tmp/Prover9_6952_n015.cluster.edu
% 0.47/1.04
% 0.47/1.04 set(prolog_style_variables).
% 0.47/1.04 set(auto2).
% 0.47/1.04 % set(auto2) -> set(auto).
% 0.47/1.04 % set(auto) -> set(auto_inference).
% 0.47/1.04 % set(auto) -> set(auto_setup).
% 0.47/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.47/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.47/1.04 % set(auto) -> set(auto_limits).
% 0.47/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.47/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.47/1.04 % set(auto) -> set(auto_denials).
% 0.47/1.04 % set(auto) -> set(auto_process).
% 0.47/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.47/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.47/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.47/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.47/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.47/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.47/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.47/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.47/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.47/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.47/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.47/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.47/1.04 % set(auto2) -> assign(stats, some).
% 0.47/1.04 % set(auto2) -> clear(echo_input).
% 0.47/1.04 % set(auto2) -> set(quiet).
% 0.47/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.47/1.04 % set(auto2) -> clear(print_given).
% 0.47/1.04 assign(lrs_ticks,-1).
% 0.47/1.04 assign(sos_limit,10000).
% 0.47/1.04 assign(order,kbo).
% 0.47/1.04 set(lex_order_vars).
% 0.47/1.04 clear(print_given).
% 0.47/1.04
% 0.47/1.04 % formulas(sos). % not echoed (14 formulas)
% 0.47/1.04
% 0.47/1.04 ============================== end of input ==========================
% 0.47/1.04
% 0.47/1.04 % From the command line: assign(max_seconds, 300).
% 0.47/1.04
% 0.47/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.47/1.04
% 0.47/1.04 % Formulas that are not ordinary clauses:
% 0.47/1.04 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 2 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 3 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 4 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 5 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 7 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 11 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 14 -(all X0 (join(complement(composition(X0,top)),composition(complement(composition(X0,top)),top)) = composition(complement(composition(X0,top)),top) & join(composition(complement(composition(X0,top)),top),complement(composition(X0,top))) = complement(composition(X0,top)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.22/2.49
% 2.22/2.49 ============================== end of process non-clausal formulas ===
% 2.22/2.49
% 2.22/2.49 ============================== PROCESS INITIAL CLAUSES ===============
% 2.22/2.49
% 2.22/2.49 ============================== PREDICATE ELIMINATION =================
% 2.22/2.49
% 2.22/2.49 ============================== end predicate elimination =============
% 2.22/2.49
% 2.22/2.49 Auto_denials:
% 2.22/2.49 % copying label goals to answer in negative clause
% 2.22/2.49
% 2.22/2.49 Term ordering decisions:
% 2.22/2.49 Function symbol KB weights: one=1. top=1. zero=1. c1=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 2.22/2.49
% 2.22/2.49 ============================== end of process initial clauses ========
% 2.22/2.49
% 2.22/2.49 ============================== CLAUSES FOR SEARCH ====================
% 2.22/2.49
% 2.22/2.49 ============================== end of clauses for search =============
% 2.22/2.49
% 2.22/2.49 ============================== SEARCH ================================
% 2.22/2.49
% 2.22/2.49 % Starting search at 0.01 seconds.
% 2.22/2.49
% 2.22/2.49 Low Water (keep): wt=38.000, iters=3354
% 2.22/2.49
% 2.22/2.49 Low Water (keep): wt=35.000, iters=3378
% 2.22/2.49
% 2.22/2.49 Low Water (keep): wt=32.000, iters=3358
% 2.22/2.49
% 2.22/2.49 Low Water (keep): wt=31.000, iters=3407
% 2.22/2.49
% 2.22/2.49 Low Water (keep): wt=30.000, iters=3370
% 2.22/2.49
% 2.22/2.49 Low Water (keep): wt=29.000, iters=3336
% 2.22/2.49
% 2.22/2.49 Low Water (keep): wt=28.000, iters=3339
% 2.22/2.49
% 2.22/2.49 Low Water (keep): wt=27.000, iters=3406
% 2.22/2.49
% 2.22/2.49 Low Water (keep): wt=26.000, iters=3336
% 2.22/2.49
% 2.22/2.49 Low Water (keep): wt=25.000, iters=3366
% 2.22/2.49
% 2.22/2.49 Low Water (keep): wt=24.000, iters=3335
% 2.22/2.49
% 2.22/2.49 ============================== PROOF =================================
% 2.22/2.49 % SZS status Theorem
% 2.22/2.49 % SZS output start Refutation
% 2.22/2.49
% 2.22/2.49 % Proof 1 at 1.41 (+ 0.05) seconds: goals.
% 2.22/2.49 % Length of proof is 129.
% 2.22/2.49 % Level of proof is 32.
% 2.22/2.49 % Maximum clause weight is 34.000.
% 2.22/2.49 % Given clauses 514.
% 2.22/2.49
% 2.22/2.49 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 2 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 3 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 4 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 5 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 7 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 11 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 2.22/2.49 14 -(all X0 (join(complement(composition(X0,top)),composition(complement(composition(X0,top)),top)) = composition(complement(composition(X0,top)),top) & join(composition(complement(composition(X0,top)),top),complement(composition(X0,top))) = complement(composition(X0,top)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.22/2.49 15 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 2.22/2.49 16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 2.22/2.49 17 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 2.22/2.49 18 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 2.22/2.49 19 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 2.22/2.49 20 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 2.22/2.49 21 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 2.22/2.49 22 join(converse(A),converse(B)) = converse(join(A,B)). [copy(21),flip(a)].
% 2.22/2.49 23 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 2.22/2.49 24 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(23),flip(a)].
% 2.22/2.49 25 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 2.22/2.49 26 join(A,join(B,C)) = join(C,join(A,B)). [copy(25),rewrite([19(2)]),flip(a)].
% 2.22/2.49 27 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 2.22/2.49 28 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 2.22/2.49 29 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(28),flip(a)].
% 2.22/2.49 30 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 2.22/2.49 31 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(30),rewrite([19(7)]),flip(a)].
% 2.22/2.49 32 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 2.22/2.49 33 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(32),rewrite([19(6),19(8)]),rewrite([19(6)])].
% 2.22/2.49 34 composition(complement(composition(c1,top)),top) != join(complement(composition(c1,top)),composition(complement(composition(c1,top)),top)) | complement(composition(c1,top)) != join(composition(complement(composition(c1,top)),top),complement(composition(c1,top))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)].
% 2.22/2.49 35 join(complement(composition(c1,top)),composition(complement(composition(c1,top)),top)) != composition(complement(composition(c1,top)),top) | join(complement(composition(c1,top)),composition(complement(composition(c1,top)),top)) != complement(composition(c1,top)) # answer(goals). [copy(34),rewrite([19(33)]),flip(a),flip(b)].
% 2.22/2.49 36 complement(top) = zero. [back_rewrite(18),rewrite([20(2),17(4)])].
% 2.22/2.49 38 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(16(a,1),24(a,1,1)),flip(a)].
% 2.22/2.49 39 converse(composition(converse(A),B)) = composition(converse(B),A). [para(16(a,1),24(a,1,2)),flip(a)].
% 2.22/2.49 40 join(A,join(B,complement(A))) = join(B,top). [para(17(a,1),26(a,2,2)),rewrite([19(2)])].
% 2.22/2.49 41 composition(A,composition(one,B)) = composition(A,B). [para(15(a,1),27(a,1,1)),flip(a)].
% 2.22/2.49 43 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(24(a,1),29(a,1,1)),rewrite([19(7)])].
% 2.22/2.49 45 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(27(a,1),29(a,1,1)),rewrite([19(6)])].
% 2.22/2.49 47 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(15(a,1),31(a,1,2,2,1))].
% 2.22/2.49 48 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A). [para(16(a,1),31(a,1,2,1))].
% 2.22/2.49 50 join(complement(converse(A)),composition(B,complement(converse(composition(A,B))))) = complement(converse(A)). [para(24(a,1),31(a,1,2,2,1)),rewrite([16(4)])].
% 2.22/2.49 51 join(complement(A),composition(converse(composition(B,C)),complement(composition(B,composition(C,A))))) = complement(A). [para(27(a,1),31(a,1,2,2,1))].
% 2.22/2.49 52 join(zero,complement(join(complement(A),complement(A)))) = A. [para(17(a,1),33(a,1,1,1)),rewrite([36(2)])].
% 2.22/2.49 56 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(33(a,1),33(a,1,2,1)),rewrite([19(10)])].
% 2.22/2.49 58 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(36(a,1),31(a,1,1)),rewrite([36(9)])].
% 2.22/2.49 60 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(36(a,1),33(a,1,2,1,1))].
% 2.22/2.49 69 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(38(a,1),22(a,1,1)),rewrite([19(7)]),flip(a)].
% 2.22/2.49 73 composition(converse(one),A) = A. [para(15(a,1),39(a,1,1)),rewrite([16(2)]),flip(a)].
% 2.22/2.49 79 converse(one) = one. [para(73(a,1),15(a,1)),flip(a)].
% 2.22/2.49 81 composition(join(A,one),B) = join(B,composition(A,B)). [para(73(a,1),29(a,1,1)),rewrite([79(4),19(4)]),flip(a)].
% 2.22/2.49 83 join(complement(A),complement(composition(one,A))) = complement(A). [para(73(a,1),31(a,1,2))].
% 2.22/2.49 84 composition(one,A) = A. [para(73(a,1),41(a,2)),rewrite([79(2),41(4)])].
% 2.22/2.49 85 join(complement(A),complement(A)) = complement(A). [back_rewrite(83),rewrite([84(3)])].
% 2.22/2.49 86 join(zero,complement(complement(A))) = A. [back_rewrite(52),rewrite([85(4)])].
% 2.22/2.49 87 converse(join(A,one)) = join(one,converse(A)). [para(79(a,1),22(a,1,1)),rewrite([19(5)]),flip(a)].
% 2.22/2.49 91 join(top,complement(A)) = top. [para(85(a,1),40(a,1,2)),rewrite([17(2),19(4)]),flip(a)].
% 2.22/2.49 92 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(60),rewrite([91(3),36(2)])].
% 2.22/2.49 93 join(top,top) = join(A,top). [para(91(a,1),40(a,1,2)),flip(a)].
% 2.22/2.49 98 join(A,top) = join(B,top). [para(93(a,1),40(a,2)),rewrite([91(3)])].
% 2.22/2.49 99 join(A,top) = c_0. [new_symbol(98)].
% 2.22/2.49 102 join(A,join(B,complement(A))) = c_0. [back_rewrite(40),rewrite([99(5)])].
% 2.22/2.49 108 converse(join(A,composition(A,B))) = composition(join(one,converse(B)),converse(A)). [para(84(a,1),43(a,1,2)),rewrite([19(4),22(4)])].
% 2.22/2.49 113 c_0 = top. [para(86(a,1),102(a,1,2)),rewrite([19(2),17(2)]),flip(a)].
% 2.22/2.49 114 join(A,join(B,complement(A))) = top. [back_rewrite(102),rewrite([113(4)])].
% 2.22/2.49 116 join(A,top) = top. [back_rewrite(99),rewrite([113(3)])].
% 2.22/2.49 127 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))). [para(87(a,1),24(a,1,1))].
% 2.22/2.49 134 converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))). [back_rewrite(108),rewrite([127(8)]),flip(a)].
% 2.22/2.49 141 join(zero,complement(A)) = complement(A). [para(86(a,1),92(a,1,2,1))].
% 2.22/2.49 142 complement(complement(A)) = A. [back_rewrite(92),rewrite([141(4),141(4)])].
% 2.22/2.49 143 join(A,zero) = A. [back_rewrite(86),rewrite([142(3),19(2)])].
% 2.22/2.49 148 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(142(a,1),33(a,1,1,1,2)),rewrite([142(5),19(4)])].
% 2.22/2.49 149 complement(zero) = top. [para(36(a,1),142(a,1,1))].
% 2.22/2.49 150 join(A,A) = A. [para(142(a,1),85(a,1,1)),rewrite([142(2),142(3)])].
% 2.22/2.49 154 join(A,join(A,B)) = join(A,B). [para(150(a,1),26(a,1)),rewrite([19(3),26(4,R),19(3),26(3,R),150(2)]),flip(a)].
% 2.22/2.49 155 join(A,complement(join(B,complement(A)))) = A. [para(33(a,1),154(a,1,2)),rewrite([19(4),33(12)])].
% 2.22/2.49 157 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(155(a,1),26(a,2,2)),rewrite([19(4),19(6)])].
% 2.22/2.49 160 join(complement(A),complement(join(A,B))) = complement(A). [para(142(a,1),155(a,1,2,1,2)),rewrite([19(2)])].
% 2.22/2.49 168 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(142(a,1),47(a,1,2,2))].
% 2.22/2.49 171 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(22(a,1),160(a,1,2,1))].
% 2.22/2.49 182 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(58(a,1),22(a,2,1)),rewrite([39(8)])].
% 2.22/2.49 222 join(complement(one),converse(complement(one))) = complement(one). [para(15(a,1),168(a,1,2))].
% 2.22/2.49 226 converse(complement(one)) = complement(one). [para(222(a,1),22(a,2,1)),rewrite([16(7),19(6),222(6)]),flip(a)].
% 2.22/2.49 231 converse(top) = top. [para(226(a,1),87(a,2,2)),rewrite([19(4),17(4),17(6)])].
% 2.22/2.49 235 join(top,converse(A)) = top. [para(231(a,1),22(a,1,1)),rewrite([19(5),116(5),231(5)])].
% 2.22/2.49 236 converse(composition(A,top)) = composition(top,converse(A)). [para(231(a,1),24(a,1,1)),flip(a)].
% 2.22/2.49 244 join(top,composition(A,converse(B))) = top. [para(38(a,1),235(a,1,2))].
% 2.22/2.49 246 join(top,composition(A,B)) = top. [para(16(a,1),244(a,1,2,2))].
% 2.22/2.49 262 composition(top,join(one,converse(A))) = top. [para(87(a,1),236(a,2,2)),rewrite([81(4),246(4),231(2)]),flip(a)].
% 2.22/2.49 267 composition(top,join(A,one)) = top. [para(16(a,1),262(a,1,2,2)),rewrite([19(3)])].
% 2.22/2.49 277 composition(top,top) = top. [para(226(a,1),262(a,1,2,2)),rewrite([17(5)])].
% 2.22/2.49 279 composition(top,composition(top,A)) = composition(top,A). [para(277(a,1),27(a,1,1)),flip(a)].
% 2.22/2.49 291 join(zero,composition(A,zero)) = zero. [para(267(a,1),50(a,1,2,2,1,1)),rewrite([231(2),36(2),231(5),36(5),81(5),154(6),231(6),36(6)])].
% 2.22/2.49 300 join(complement(A),complement(join(B,A))) = complement(A). [para(155(a,1),56(a,2)),rewrite([142(2),142(4),142(8),56(13)])].
% 2.22/2.49 306 join(A,composition(B,zero)) = A. [para(291(a,1),26(a,1,2)),rewrite([143(2),143(4),19(3)]),flip(a)].
% 2.22/2.49 310 composition(join(A,B),zero) = composition(A,zero). [para(306(a,1),29(a,1)),flip(a)].
% 2.22/2.49 312 composition(A,zero) = zero. [para(306(a,1),81(a,2)),rewrite([310(4)])].
% 2.22/2.49 314 composition(converse(zero),A) = converse(zero). [para(312(a,1),39(a,1,1)),flip(a)].
% 2.22/2.49 323 composition(join(A,composition(B,converse(zero))),C) = join(composition(B,converse(zero)),composition(A,C)). [para(314(a,1),45(a,1,1,2)),flip(a)].
% 2.22/2.49 327 converse(zero) = zero. [para(314(a,1),312(a,1))].
% 2.22/2.49 330 join(zero,composition(A,B)) = composition(A,B). [back_rewrite(323),rewrite([327(2),312(2),143(2),327(3),312(3)]),flip(a)].
% 2.22/2.49 332 composition(zero,A) = zero. [back_rewrite(314),rewrite([327(2),327(4)])].
% 2.22/2.49 333 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(182),rewrite([327(2),330(7),327(7)])].
% 2.22/2.49 391 composition(top,complement(composition(top,A))) = complement(composition(top,A)). [para(279(a,1),31(a,1,2,2,1)),rewrite([231(5),81(9,R),19(3),116(3)])].
% 2.22/2.49 395 join(complement(A),complement(composition(top,A))) = complement(A). [para(279(a,1),51(a,1,2,2,1)),rewrite([277(4),231(3),391(6)])].
% 2.22/2.49 418 composition(converse(complement(composition(A,top))),composition(A,B)) = zero. [para(333(a,1),27(a,1,1)),rewrite([332(2)]),flip(a)].
% 2.22/2.49 561 join(one,complement(composition(converse(complement(A)),A))) = complement(composition(converse(complement(A)),A)). [para(168(a,1),300(a,1,2,1)),rewrite([142(7),19(6)])].
% 2.22/2.49 598 join(A,composition(top,A)) = composition(top,A). [para(395(a,1),155(a,1,2,1)),rewrite([142(4),19(3)])].
% 2.22/2.49 629 join(A,composition(A,top)) = composition(A,top). [para(598(a,1),69(a,1,1)),rewrite([38(4),231(2),231(4),16(6),19(5)]),flip(a)].
% 2.22/2.49 630 composition(complement(composition(c1,top)),top) != complement(composition(c1,top)) # answer(goals). [back_rewrite(35),rewrite([629(11),629(24)]),xx(a)].
% 2.22/2.49 1510 composition(A,join(B,one)) = join(A,composition(A,B)). [para(134(a,1),16(a,1,1)),rewrite([16(4)]),flip(a)].
% 2.22/2.49 1970 composition(complement(A),complement(composition(converse(complement(A)),A))) = complement(A). [para(1510(a,2),48(a,1)),rewrite([19(7),561(7)])].
% 2.22/2.49 2513 join(A,complement(join(A,B))) = join(A,complement(B)). [para(148(a,1),157(a,1,2)),flip(a)].
% 2.22/2.49 2941 join(complement(converse(A)),converse(join(A,B))) = top. [para(171(a,1),114(a,1,2)),rewrite([19(5)])].
% 2.22/2.49 2967 join(A,join(B,converse(complement(converse(A))))) = top. [para(2941(a,1),22(a,2,1)),rewrite([16(6),26(5),19(4),26(5,R),19(4),231(7)])].
% 2.22/2.49 2998 join(A,converse(complement(converse(A)))) = top. [para(150(a,1),2967(a,1,2))].
% 2.22/2.49 3035 join(A,complement(converse(complement(converse(A))))) = A. [para(2998(a,1),2513(a,1,2,1)),rewrite([36(2),143(2)]),flip(a)].
% 2.22/2.49 3036 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(16(a,1),3035(a,1,2,1,1,1))].
% 2.22/2.49 3039 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(3035(a,1),33(a,1,2,1)),rewrite([142(9),19(8),2513(8),142(6)])].
% 2.22/2.49 3158 converse(complement(converse(complement(A)))) = A. [para(3036(a,1),22(a,2,1)),rewrite([16(2),3039(5),16(6)])].
% 2.22/2.49 3181 complement(converse(complement(A))) = converse(A). [para(3158(a,1),16(a,1,1)),flip(a)].
% 2.22/2.49 3250 converse(complement(A)) = complement(converse(A)). [para(3181(a,1),142(a,1,1)),flip(a)].
% 2.22/2.49 3358 composition(complement(A),complement(composition(complement(converse(A)),A))) = complement(A). [back_rewrite(1970),rewrite([3250(3)])].
% 2.22/2.49 3428 composition(complement(composition(top,converse(A))),composition(A,B)) = zero. [back_rewrite(418),rewrite([3250(4),236(3)])].
% 2.22/2.49 9382 composition(complement(composition(A,top)),top) = complement(composition(A,top)). [para(236(a,1),3358(a,1,2,1,1,1)),rewrite([3428(10),149(5)])].
% 2.22/2.49 9383 $F # answer(goals). [resolve(9382,a,630,a)].
% 2.22/2.49
% 2.22/2.49 % SZS output end Refutation
% 2.22/2.49 ============================== end of proof ==========================
% 2.22/2.49
% 2.22/2.49 ============================== STATISTICS ============================
% 2.22/2.49
% 2.22/2.49 Given=514. Generated=69510. Kept=9361. proofs=1.
% 2.22/2.49 Usable=417. Sos=7403. Demods=7392. Limbo=9, Disabled=1545. Hints=0.
% 2.22/2.49 Megabytes=11.78.
% 2.22/2.49 User_CPU=1.41, System_CPU=0.05, Wall_clock=2.
% 2.22/2.49
% 2.22/2.49 ============================== end of statistics =====================
% 2.22/2.49
% 2.22/2.49 ============================== end of search =========================
% 2.22/2.49
% 2.22/2.49 THEOREM PROVED
% 2.22/2.49 % SZS status Theorem
% 2.22/2.49
% 2.22/2.49 Exiting with 1 proof.
% 2.22/2.49
% 2.22/2.49 Process 7106 exit (max_proofs) Fri Jul 8 08:29:23 2022
% 2.22/2.49 Prover9 interrupted
%------------------------------------------------------------------------------